Rewrite as a simplified fraction. ${0.87\overline{2} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 872.2222...\\ 100x &= 87.2222...\end{align*}}$ Subtracting the two equations, we have: ${900x = 785}$ ${x = \dfrac{785}{900}} $ ${x = \dfrac{157}{180}} $